标题： 多维筛选中的极值点 显示英文标题

标题： Extreme Points in Multi-Dimensional Screening

摘要： 本文表征了线性效用筛选问题中激励相容机制集合的极点。 极点是完全机制，这意味着它们的菜单不能被缩放和平移以使额外的可行性约束生效。 在类型为一维的问题中，极点可以以菜单大小的紧上界进行易于处理的描述。 在类型为多维的问题中，通过应用任意小的扰动，每个完全机制都可以转换为一个极点。 对于具有有限菜单的机制，这种扰动会将菜单项移动到一般位置。 一般的完全机制是具有不可数菜单的极点。 在委托、否决谈判和垄断问题的应用中，类似的结果成立，我们考虑的是特定类别的目标泛函的唯一最大化机制。 证明涉及极端点的菜单与不可分解凸体之间的一个新联系，这一联系最初由Gale（1954）研究。 显示英文摘要

摘要： This paper characterizes extreme points of the set of incentive-compatible mechanisms for screening problems with linear utility. Extreme points are exhaustive mechanisms, meaning their menus cannot be scaled and translated to make additional feasibility constraints binding. In problems with one-dimensional types, extreme points admit a tractable description with a tight upper bound on their menu size. In problems with multi-dimensional types, every exhaustive mechanism can be transformed into an extreme point by applying an arbitrarily small perturbation. For mechanisms with a finite menu, this perturbation displaces the menu items into general position. Generic exhaustive mechanisms are extreme points with an uncountable menu. Similar results hold in applications to delegation, veto bargaining, and monopoly problems, where we consider mechanisms that are unique maximizers for specific classes of objective functionals. The proofs involve a novel connection between menus of extreme points and indecomposable convex bodies, first studied by Gale (1954).